A small coil C with N $$=$$ $$200$$ turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in figure. The cross sectional area of coil is $$A=1.0$$ $$cm2$$, length of arm OA of the balance beam is l $$=$$ $$30$$ cm. When there is no current in the coil the balance is in equilibrium. On passing a current I $$=$$ $$22$$ mA through the coil the equilibrium is restored by putting the additional counter weight of mass ∆$$m=60$$ mg on the balance pan. Find the magnetic induction at the spot where coil is located.

Question

A small coil C with N $$=$$ $$200$$ turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in figure. The cross sectional area of coil is $$A=1.0$$ $$cm2$$, length of arm OA of the balance beam is l $$=$$ $$30$$ cm. When there is no current in the coil the balance is in equilibrium. On passing a current I $$=$$ $$22$$ mA through the coil the equilibrium is restored by putting the additional counter weight of mass ∆$$m=60$$ mg on the balance pan. Find the magnetic induction at the spot where coil is located.

Infinity Learn · Accepted Answer

On passing current through the coil, it acts as a magnetic dipole. Torque acting on magnetic dipole is counter balanced by the moment of additional weight about position O. Torque acting on a magnetic dipoleτ$$=MB$$ $$sin$$ θ$$=NiAB$$ $$sin$$ $$90o=NiABAgain$$, τ $$=$$ Force x Lever arm $$=$$ ∆mg x l⇒NiAB $$=$$ ∆mgl⇒$$B=$$∆$$mglNiA=60$$ x $$10-3$$ x $$9.8$$ x $$30$$ x $$10-2200$$ x $$22$$ x $$10-3$$ x $$1$$ x $$10-4=0.4$$ T

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